Entropy-based grid approach for handling outliers: a case study to environmental monitoring data

Grid-based approaches render an efficient framework for data clustering in the presence of incomplete, inexplicit, and uncertain data. This paper proposes an entropy-based grid approach (EGO) for outlier detection in clustered data. The given hard clusters obtained from a hard clustering algorithm, EGO uses entropy on the dataset as a whole or on an individual cluster to detect outliers. EGO works in two steps: explicit outlier detection and implicit outlier detection. Explicit outlier detection is concerned with those data points that are isolated in the grid cells. They are either far from the dense region or maybe a nearby isolated data point and therefore declared as an explicit outlier. Implicit outlier detection is associated with the detection of outliers that are perplexedly deviated from the normal pattern. The determination of such outliers is achieved using entropy change of the dataset or a specific cluster for each deviation. The elbow based on the trade-off between entropy and object geometries optimizes the outlier detection process. Experimental results on CHAMELEON datasets and other similar datasets suggested that the proposed approach(es) detect the outliers more precisely and extend the capability of outliers detection to an additional 4.5% to 8.6%. Moreover, the resultant clusters became more precise and compact when the entropy-based gridding approach is applied on top of hard clustering algorithms. The performance of the proposed algorithms is compared with well-known outlier detection algorithms, including DBSCAN, HDBSCAN, RE3WC, LOF, LoOP, ABOD, CBLOF and HBOS. Finally, a case study for detecting outliers in environmental data has been carried out using the proposed approach and results are generated on our synthetically prepared datasets. The performance shows that the proposed approach may be an industrial-oriented solution to outlier detection in environmental monitoring data.